How do you differentiate f(x)=x^3-x^2+4x-1 using the sum rule? Calculus Basic Differentiation Rules Sum Rule 1 Answer Lucio Falabella Jan 18, 2016 f'(x)=3x^2-2x+4 Explanation: The Sum Rule says: d/dxsum_(i=1)^nk_i*f_i(x)=d/dx[k_1f_1(x)+k_2f_2(x)+...+k_nf_n(x)]= =k_isum_(i=1)^nd/dxf_i(x)=k_1f_1'(x)+k_2f_2'(x)+...+k_nf_n'(x) :.f'(x)=d/dx(x^3)-1*d/dx(x^2)+4d/dx(x)-1d/dx(1)= =3x^(3-1)-1*(2x^(2-1))+4*(1)-1*(0)= =3x^2-2x+4 Answer link Related questions What is the Sum Rule for derivatives? How do you find the derivative of y=f(x)+g(x)? How do you find the derivative of y = f(x) - g(x)? What is the derivative of f(x) = xlnx-lnx^x? How do you differentiate f(x)=1/x+1/x^3 using the sum rule? How do you differentiate f(x)=x+x-2x using the sum rule? How do you differentiate f(x)=x^2-x-x(x-1) using the sum rule? How do you differentiate f(x)=sinx+cosx-x^3 using the sum rule? How do you differentiate f(x)=x+lnx^2-x^2 using the sum rule? How do you differentiate f(x)=1/sinx-secx+tanx using the sum rule? See all questions in Sum Rule Impact of this question 3264 views around the world You can reuse this answer Creative Commons License